Electronic spectra approximate calculation

The CASSCF/CASPT2 calculations were performed with an active space including the five nd, the (n + l)s, the three (n+ l)p orbitals, and a second set of nd orbitals to account for the double shell effect. The importance of including a second 3d shell in the active space was detected in an early study of the electronic spectrum of the nickel atom [2]. This had already been suggested from MRCI results [1]. The results obtained by RT at about the same time indicated that such effects are effectively accounted for when a method is used that includes cluster corrections to all orders, like the QCI method used by them [3]. This result will hold true also for the less approximate coupled cluster method CCSD(T). 

Analytic, exact solutions cannot be obtained except for the simplest systems, i.e. hydrogen-like atoms with just one electron and one nucleus. Good approximate solutions can be found by means of the self-consistent field (SCF) method, the details of which need not concern us. If all the electrons have been explicitly considered in the Hamiltonian, the wave functions V, will be many-electron functions V, will contain the coordinates of all the electrons, and a complete electron density map can be obtained by plotting Vf. The associated energies E, are the energy states of the molecule (see Section 2.6) the lowest will be the ground state , and the calculated energy differences En — El should match the spectroscopic transitions in the electronic spectrum. 

Basically there are two main nonequilibrium effects the electronic spectrum modification and excitation of vibrons (quantum vibrations). In the weak electron-vibron coupling case the spectrum modification is usually small (which is dependent, however, on the vibron dissipation rate, temperature, etc.) and the main possible nonequilibrium effect is the excitation of vibrons at finite voltages. We have developed an analytical theory for this case [124]. This theory is based on the self-consistent Born approximation (SCBA), which allows to take easily into account and calculate nonequilibrium distribution functions of electrons and vibrons. 

The majority of photochemistry of course deals with nondegenerate states, and here vibronic coupling effects are also found. A classic example of non-Jahn-Teller vibronic coupling is found in the photoelectron spectrum of butatriene, formed by ejection of electrons Irom the electronic eigenfunctions (approximately the molecular orbitals). Bands due to the ground and first excited A B2u states of the radical cation are found at energies predicted by calculations. Between the bands, however, is a further band, which was termed the mystery band [169]. This band was then shown to be due to vibronic coupling between the states [170]. 

The geometrical structure of gaseous PH2 in its X Ai ground state appears to be similar to that of ground-state PH2 (with an internuclear distance of r=1.42 A and an interbond angle of a = 92° see p. 72). This was inferred from a sharp increase of the photodetachment cross section at threshold, measured by ion cyclotron resonance [2, 3] and from the predominance of the (0, 0, 0)<-(0, 0, 0) transition in the PH2, X Bi PH, X A photoelectron spectrum [4]. r=1.34 0.05 A and a = 92 5 were taken from the isoelectronic H2S molecule (and used to calculate the thermodynamic functions of PH, see p. 109) [5]. r and a have also been theoretically calculated by several ab initio MO methods, i.e., at an MP2 [6, 7], a CEPA (coupled electron pair approximation) [8], and an HF level [9 to 15]. r was also obtained from a united-atom approximation [16] a was also calculated by a semiempirical (CNDO/2) method [17] and estimated by extended Huckel calculations [18]. 

Kotzian et al. (1991) and Kotzian and Rosch (1992) applied their INDO/1 and INDO/S-CI methods to hydrated cerium(III), i.e. model complexes [Ce(H20) ] (n=8,9), in order to rationalize the electronic structure and the electronic spectrum of these species. Besides the scalar relativistic effects spin-orbit coupling was also included in the INDO/S-CI studies. The spin-orbit splitting of the 4f F and 5d states of the free Ce " ion was calculated as 2175cm" and 2320cm in excellent agreement with the experimental values of 2253 cm and 2489 cm" , respectively. The calculated energy separation between the F and states of approximately 44000cm" (estimated fi-om fig. 5 in Kotzian and Rosch 1992) is somewhat lower than the experimental value of 49943 cm" (Martin et al. 1978). 

As is seen, the direct action of radiation on HNO3 leads to the formation of only one radical NO3 (reaction (Equation 4.7) per one acid molecnle destroyed in the reaction (Equation 4.19), whereas the pulse radiolysis of less concentrated solutions produces two radicals NO3 according to reactions (Equation 4.15)-(Equation 4.18). The evidence for the reaction (Equation 4.19) is the absorption band of NO at 400 nm [14] in an optical spectrum appearing in 15 M HNO3 immediately after advancing the electronic pulse. Such absorption was not observed for diluted 3M solutions. The approximate calculation of the NO3 radiation yield for 5-8 M solutions of HNO3 gives a minimum value of 10 radicals per 100 eV [10]. The yield of direct radiation decomposition of nitrate anions was estimated to be 8-17 ions per 100 eV [11]. 

Table 2 shows some electronic parameters extracted from the band structure spectrum. The calculated bandwidth of the highest occupied band is 3.5 eV, the band gap is 2.8 eV, and the ionization potential, IP, is 6.0 eV. Despite the approximation of considering the polymer as being planar, all the electronic parameters are in good agreement with those determined experimentally [12,13,35,47,48]. The inclusion of electronic correlation in these calculations seems to be the key factor in the accuracy of the predicted results. 

A recent analysis of the electronic spectrum of aniline, however, suggests that here the harmonic oscillator approximation is incorrect, and so the calculated functions for aniline may be in error. 

---